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%% Evaluate Double Integral in Polar Coordinates %% % Define the function % % $$f \left( \theta,r \right) = \frac{r}{\sqrt{r \cos \theta + r \sin % \theta} \left( 1+r \cos \theta + r \sin \theta \right) ^2}$$ % fun = @(x,y) 1./( sqrt(x + y) .* (1 + x + y).^2 ); polarfun = @(theta,r) fun(r.*cos(theta),r.*sin(theta)).*r; %% % Define a function for the upper limit of $r$. rmax = @(theta) 1./(sin(theta) + cos(theta)); %% % Integrate over the region bounded by $0 \le \theta \le \pi/2$ and $0 \le % r \le r_{max}$. q = integral2(polarfun,0,pi/2,0,rmax)